ali's father was five times as old as Ali 7 1/2 years ago.After 7 1/2 years father will be twice as old as ALI .what are their present ages?

To solve this problem, let's assign variables to represent Ali's age and his father's age. Let's assume Ali's current age is "x," and his father's current age is "5x" (since his father was five times older than Ali 7 1/2 years ago).

7 1/2 years ago, Ali's age would have been x - 7.5, and his father's age would have been 5x - 7.5 (since his father was five times older than Ali).

After 7 1/2 years:
Ali's age would be x + 7.5
Father's age would be 5x + 7.5

According to the problem, the father will be twice as old as Ali after 7 1/2 years. So we can set up an equation:

5x + 7.5 = 2(x + 7.5)

Now, let's solve the equation:

5x + 7.5 = 2x + 15

Subtract 2x from both sides:

3x + 7.5 = 15

Subtract 7.5 from both sides:

3x = 7.5

Divide both sides by 3:

x = 2.5

So Ali's current age (x) is 2.5 years.

To find the father's current age, substitute x back into 5x:

Father's current age = 5 * 2.5 = 12.5 years.

Therefore, Ali's present age is 2.5 years, and his father's present age is 12.5 years.